Abstract
Is there an Edge of Chaos, and if so, can evolution take us to it? Many issues have to be settled before any definitive answer can be given. For quantitative work, we need a good measure of complexity. We suggest that convergence time is an appropriate and useful measure. In the case of cellular automata, one of the advantages of the convergence-time measure is that it can be analytically approximated using a generalized mean field theory.
In this paper we demonstrate that the mean field theory for cellular automata can 1) reduce the variablity of behavior inherent in the λ-parameter approach, 2) approximate convergence time, and 3) drive an evolutionary process toward increasing complexity.
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Rajarshi Das, Melanie Mitchell, and James P. Crutchfield. A genetic algorithm discovers particle-based computation in cellular automata. In Proceedings of the Third Parallel Problem-Solving From Nature, march 1994.
W. Li et al. Transition phenomena in CA rule space. Physica D, 45:77, 1990.
Howard Gutowitz. Introduction (to cellular automata). Physica D, 45:vii, 1990.
H. A. Gutowitz, J. D. Victor, and B. W. Knight. Local structure theory for cellular automata. Physica D, 28:18–48, 1987.
J.H. Holland. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI, 1975.
Kunihiko Kaneko and Junji Suzuki. Evolution toward the edge of chaos in an imitation game. In Langton et al., editor, Artificial Life III. Adddison-Wesley, 1993.
Christopher G. Langton. Studying artificial life with cellular automata. Physica D, 22:120–149, 1986.
C. G. Langton. Computation at the edge of chaos. Physica D, 42, 1990.
Melanie Mitchell, James P. Crutchfield, and Peter T. Hraber. Dynamics, computation, and the edge of chaos: A re-examination. In G. Cowan, D. Pines, and D. Melzner, editors, Complexity:Metaphors, Models, and Reality, volume 19, Reading, MA, 1994. Santa Fe Institute Studies in the Sciences of Complexity, Proceedings, Addison-Wesley.
Melanie Mitchell, Peter T. Hraber, and James P. Crutchfield. Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems, 7:89–130, 1993.
N. H. Packard. Adaptation toward the edge of chaos. In A. J. Mandell J. A. S. Kelso and M. F. Shlesinger, editors, Dynamic Patterns in Complex Systems, pages 293–301, Singapore, 1988. World Scientific.
Junji Suzuki and Kunihiko Kaneko. Imitation games. Physica D, 75:328–342, 1994.
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© 1995 Springer-Verlag Berlin Heidelberg
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Gutowitz, H., Langton, C. (1995). Mean field theory of the Edge of Chaos. In: Morán, F., Moreno, A., Merelo, J.J., Chacón, P. (eds) Advances in Artificial Life. ECAL 1995. Lecture Notes in Computer Science, vol 929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59496-5_288
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DOI: https://doi.org/10.1007/3-540-59496-5_288
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